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user186505
user186505

I found this question in a previous test paper:

enter image description here

I'm having a few confusions:

  1. Low pass filters are supposed to block signals abovebelow a certain frequency. Here that certain frequency is \$w_c=a\$. I'm not sure how to approach this problem. What would be the frequency of \$v(t) = e^{-at}\$? Wolfram Alpha says that the Fourier transform of functions of the form \$e^{-at}\$ do not have any closed form. Also, Fourier series of the signal wouldn't exist since it's not periodic. So, how should I find the energy dissipated in the resistor?

  2. In the second part of the question, what exactly is meant by \$h(t)\$ and \$y(t)\$, any idea?

Please note that I've read the answers to How Fourier transform be able to deal with transients?, but it doesn't really answer my question.

I found this question in a previous test paper:

enter image description here

I'm having a few confusions:

  1. Low pass filters are supposed to block signals above a certain frequency. Here that certain frequency is \$w_c=a\$. I'm not sure how to approach this problem. What would be the frequency of \$v(t) = e^{-at}\$? Wolfram Alpha says that the Fourier transform of functions of the form \$e^{-at}\$ do not have any closed form. Also, Fourier series of the signal wouldn't exist since it's not periodic. So, how should I find the energy dissipated in the resistor?

  2. In the second part of the question, what exactly is meant by \$h(t)\$ and \$y(t)\$, any idea?

Please note that I've read the answers to How Fourier transform be able to deal with transients?, but it doesn't really answer my question.

I found this question in a previous test paper:

enter image description here

I'm having a few confusions:

  1. Low pass filters are supposed to block signals below a certain frequency. Here that certain frequency is \$w_c=a\$. I'm not sure how to approach this problem. What would be the frequency of \$v(t) = e^{-at}\$? Wolfram Alpha says that the Fourier transform of functions of the form \$e^{-at}\$ do not have any closed form. Also, Fourier series of the signal wouldn't exist since it's not periodic. So, how should I find the energy dissipated in the resistor?

  2. In the second part of the question, what exactly is meant by \$h(t)\$ and \$y(t)\$, any idea?

Please note that I've read the answers to How Fourier transform be able to deal with transients?, but it doesn't really answer my question.

edited body
Source Link
user186505
user186505

I found this question in a previous test paper:

enter image description here

I'm having a few confusions:

  1. Low pass filters are supposed to block signals belowabove a certain frequency. Here that certain frequency is \$w_c=a\$. I'm not sure how to approach this problem. What would be the frequency of \$v(t) = e^{-at}\$? Wolfram Alpha says that the Fourier transform of functions of the form \$e^{-at}\$ do not have any closed form. Also, Fourier series of the signal wouldn't exist since it's not periodic. So, how should I find the energy dissipated in the resistor?

  2. In the second part of the question, what exactly is meant by \$h(t)\$ and \$y(t)\$, any idea?

Please note that I've read the answers to How Fourier transform be able to deal with transients?, but it doesn't really answer my question.

I found this question in a previous test paper:

enter image description here

I'm having a few confusions:

  1. Low pass filters are supposed to block signals below a certain frequency. Here that certain frequency is \$w_c=a\$. I'm not sure how to approach this problem. What would be the frequency of \$v(t) = e^{-at}\$? Wolfram Alpha says that the Fourier transform of functions of the form \$e^{-at}\$ do not have any closed form. Also, Fourier series of the signal wouldn't exist since it's not periodic. So, how should I find the energy dissipated in the resistor?

  2. In the second part of the question, what exactly is meant by \$h(t)\$ and \$y(t)\$, any idea?

Please note that I've read the answers to How Fourier transform be able to deal with transients?, but it doesn't really answer my question.

I found this question in a previous test paper:

enter image description here

I'm having a few confusions:

  1. Low pass filters are supposed to block signals above a certain frequency. Here that certain frequency is \$w_c=a\$. I'm not sure how to approach this problem. What would be the frequency of \$v(t) = e^{-at}\$? Wolfram Alpha says that the Fourier transform of functions of the form \$e^{-at}\$ do not have any closed form. Also, Fourier series of the signal wouldn't exist since it's not periodic. So, how should I find the energy dissipated in the resistor?

  2. In the second part of the question, what exactly is meant by \$h(t)\$ and \$y(t)\$, any idea?

Please note that I've read the answers to How Fourier transform be able to deal with transients?, but it doesn't really answer my question.

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Post Deleted by user186505
Source Link
user186505
user186505

How to deal with low pass filter questions if Fourier transform of signal does not exist?

I found this question in a previous test paper:

enter image description here

I'm having a few confusions:

  1. Low pass filters are supposed to block signals below a certain frequency. Here that certain frequency is \$w_c=a\$. I'm not sure how to approach this problem. What would be the frequency of \$v(t) = e^{-at}\$? Wolfram Alpha says that the Fourier transform of functions of the form \$e^{-at}\$ do not have any closed form. Also, Fourier series of the signal wouldn't exist since it's not periodic. So, how should I find the energy dissipated in the resistor?

  2. In the second part of the question, what exactly is meant by \$h(t)\$ and \$y(t)\$, any idea?

Please note that I've read the answers to How Fourier transform be able to deal with transients?, but it doesn't really answer my question.